Morphological Stability of Epitaxial Thin Elastic Films by Van Der Waals Force

The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found that only van der Waals force with negative Hamaker constant (A < 0) tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film. The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.

Vibration of an Adhered Microbeam Under a Periodically Shaking Electrical Force

The vibration analysis of an adhered S-shaped microbeam under alternating sinusoidal voltage is presented. The shaking force is the electrical force due to the sinusoidal voltage. During vibration, both the microbeam deflection and the adhesion length keep changing. The microbeam deflection and adhesion length are numerically determined by the iteration method. As the adhesion length keeps changing, the domain of the equation of motion for the microbeam (unadhered part) changes correspondingly, which results in changes of the structure natural frequencies. For this reason, the system can never reach a steady state. The transient behaviors of the microbeam under different shaking frequencies are compared. We deliberately choose the initial conditions to compare our dynamic results with the existing static theory. The paper also analyzes the changing behavior of adhesion length during vibration and an asymmetric pattern of adhesion length change is revealed, which may be used to guide the dynamic de-adhering process. The abnormal behavior of the adhered microbeam vibrating at almost the same frequency under two quite different shaking frequencies is also shown. The Galerkin method is used to discretize the equation of motion and its convergence study is also presented. The model is only applicable in the case that the peel number is equal to 1. Some other model limitations are also discussed.

Combined effect of surface tension, gravity and van der Waals force induced by a non-contact probe tip on the shape of liquid surface

Aiming at understanding how a liquid film on a substrate affects the atomic force microscopic image in experiments, we present an analytical representation of the shape of liquid surface under van der Waals interaction induced by a non-contact probe tip. The analytical expression shows good consistence with the corresponding numerical results. According to the expression, we find that the vertical scale of the liquid dome is mainly governed by a combination of van der Waals force, surface tension and probe tip radius, and is weekly related to gravity. However, its horizontal extension is determined by the capillary length.

Experimental Investigation of the Velocity Effect on Adhesion Forces with an Atomic Force Microscope Atomic Force Microscope

Capillary forces are significantly dominant in adhesive forces measured with an atomic force microscope (AFM) in ambient air, which are always thought to be dependent on water film thickness, relative humidity, and the free energy of water film. We study the nature of the pull-off force on a variety of surfaces as a function of tip velocity. It is found that the capillary forces are of relatively strong dependence on tip velocity. The present experiment is expected to provide a better understanding of the work mechanism of AFM in ambient air.

Analysis of a Rubber Cone Tensioned by a Concentrated Force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180 degrees, the solution becomes that of non-linear Boussinesq's problem for tension case.

Optical Factors Determined by the T-matrix Method in Turbidity Measurement of Absolute Coagulation Rate Constants

Turbidity measurement for the absolute coagulation rate constant of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor to derive the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed in the aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion about the physical insight of using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the calculated data of the optical factor by the T-matrix method for a range of particle radii and incident light wavelengths are listed.

Competitive protein adsorption studied with atomic force microscopy and imaging ellipsometry

The adsorption and competitive adsorption of collagen and bovine serum albumin (BSA) were directly visualized and quantified using atomic force microscopy (AFM) and imaging ellipsometry. Chemically modified silicon surfaces were used as hydrophilic and hydrophobic substrates. The results showed that collagen and BSA in single component solution adsorbed onto a hydrophobic surface two times more than that onto a hydrophilic surface. The competitive adsorption between collagen and BSA showed that serum albumin preferentially adsorbed onto a hydrophobic surface, while collagen on a hydrophilic surface. In the binary solution of BSA (1 mg/ml BSA) and collagen (0.1 mg/ml), nearly 100% of the protein adsorbed onto the hydrophobic surface was BSA, but on the hydrophilic surface only about 6% was BSA. Surface affinity was the main factor controlling the competitive adsorption.

Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

Studying Aggregate in Lysozyme Solution by Atomic Force Microscope

The aggregates in lysozyme solution with different NaCl concentration were investigated by Atomic Force Microscope (AFM). The AFM images show that there exist lysozyme monomers, n-mers and clusters in lysozyme solution when the conditions are not suitable for crystal growth. In favorable conditions for crystal growth, the lysozyme clusters disappear and almost only monomers exist in solution.

Influence of Coriolis force on bulk flows during horizontal Bridgman growth on a centrifuge: a numerical study

Three-dimensional and time-dependent numerical simulations are performed For melt convection in horizontal Bridgman crystal growth tinder high gravity conditions by means of a centrifuge. The numerical results show that Coriolis Force can cause a stabilizing effect on the fluctuations of the melt flow under a specific relation direction and relation rates of the centrifuge as reported in previous experiments (Ma et al., Materials Processing in High Gravity, Plenum Press, New York, 1994, p. 61). The present simulation provides details of the now features associated with the effect of the Coriolis force. There are also some differences between the present three-dimensional and former two-dimensional numerical solutions particularly in the prediction of the critical conditions and flow patterns.

Surface Stability of Epitaxial Elastic Films by Casimir Force

We investigate the morphological stability of epitaxial thin elastic films on a substrate by the Casimir force between the film surface and a flat plate. Critical undulation wavelengths are derived for two different limit conditions. Consideration of the Casimir force in both limit cases decreases the critical wavelength of the surface perturbation.

An Approximate Method For Calculation Of Fluid Force And Response Of A Circular Cylinder At Lock-In

In this paper, equations calculating lift force of a rigid circular cyclinder at lock-in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cyclinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cyclinders and long flexible circular cyclinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results show the effectiveness of this approximate method.

The Capillary Force In Micro- And Nano-Indentation With Different Indenter Shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force. (c) 2008 Elsevier Ltd. All rights reserved.

Concentrated-Mass Cantilever Enhances Multiple Harmonics In Tapping-Mode Atomic Force Microscopy

The natural frequencies of a cantilever probe can be tuned with an attached concentrated mass to coincide with the higher harmonics generated in a tapping-mode atomic force microscopy by the nonlinear tip-sample interaction force. We provide a comprehensive map to guide the choice of the mass and the position of the attached particle in order to significantly enhance the higher harmonic signals containing information on the material properties. The first three eigenmodes can be simultaneously excited with only one carefully positioned particle of specific mass to enhance multiple harmonics. Accessing the interaction force qualitatively based on the high-sensitive harmonic signals combines the real-time material characterization with the imaging capability. (C) 2008 American Institute of Physics.